140823 - Pure point measures with sparse support and sparse Fourier-Bohr support.pdf (437.24 kB)
Pure point measures with sparse support and sparse Fourier-Bohr support
journal contribution
posted on 2023-05-20, 17:38 authored by Baake, M, Strungaru, N, Venta TeraudsVenta TeraudsFourier‐transformable Radon measures are called doubly sparse when both the measure and its transform are pure point measures with sparse support. Their structure is reasonably well understood in Euclidean space, based on the use of tempered distributions. Here, we extend the theory to second countable, locally compact Abelian groups, where we can employ general cut and project schemes and the structure of weighted model combs, along with the theory of almost periodic measures. In particular, for measures with Meyer set support, we characterise sparseness of the Fourier–Bohr spectrum via conditions of crystallographic type, and derive representations of the measures in terms of trigonometric polynomials. More generally, we analyse positive definite, doubly sparse measures in a natural cut and project setting, which results in a Poisson summation type formula.
History
Publication title
Transactions of the London Mathematical SocietyVolume
7Pagination
1-32ISSN
2052-4986Department/School
School of Natural SciencesPublisher
John Wiley & Sons LtdPlace of publication
United KingdomRights statement
Copyright 2020 The Authors. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) http://creativecommons.org/licenses/by-nc-nd/4.0/Repository Status
- Open